The complexity of many-body quantum wave functions is a central aspect of several fields of physics and chemistry where nonperturbative interactions are prominent. Artificial neural networks (ANNs) have proven to be a flexible tool to approximate quantum many-body states in condensed matter and chemistry problems. In this work we introduce a neural-network quantum state ansatz to model the ground-state wave function of light nuclei, and approximately solve the nuclear many-body Schrödinger equation. Using efficient stochastic sampling and optimization schemes, our approach extends pioneering applications of ANNs in the field, which present exponentially scaling algorithmic complexity. We compute the binding energies and point-nucleon densities of A≤4 nuclei as emerging from a leading-order pionless effective field theory Hamiltonian. We successfully benchmark the ANN wave function against more conventional parametrizations based on two- and three-body Jastrow functions, and virtually exact Green's function Monte Carlo results.
Predicting the structure of quantum many-body systems from the first principles of quantum mechanics is a common challenge in physics, chemistry, and material science. Deep machine learning has proven to be a powerful tool for solving condensed matter and chemistry problems, while for atomic nuclei it is still quite challenging because of the complicated nucleon-nucleon interactions, which strongly couple the spatial, spin, and isospin degrees of freedom. By combining essential physics of the nuclear wave functions and the strong expressive power of artificial neural networks, we develop FeynmanNet, a deep-learning variational quantum Monte Carlo approach for ab initio nuclear structure. We show that FeynmanNet can provide very accurate solutions of ground-state energies and wave functions for
4He,6Li, and even up to
16O as emerging from the leading-order and next-to-leading-order Hamiltonians of pionless effective field theory. Compared to the conventional diffusion Monte Carlo approaches, which suffer from the severe inherent fermion-sign problem, FeynmanNet reaches such a high accuracy in a variational way and scales polynomially with the number of nucleons. Therefore, it paves the way to a highly accurate and efficient ab initio method for predicting nuclear properties based on the realistic interactions between nucleons.
An efficient emulator for \emph{ab initio} calculations of nuclear ground-state properties is developed by integrating the neural-network variational Monte Carlo framework, FeynmanNet, with the eigenvector continuation. It enables the calculation of observables for different Hamiltonians with minimal computational cost, while delivering ground-state energies with errors below
0.5% compared to the full FeynmanNet results. With this emulator, the ground-state energies and charge radii of
16O,
15O,
14O,
15N, and
14C are computed using a nuclear Hamiltonian derived from the leading-order pionless effective field theory, with a large number of different values of low-energy constants (LECs). Then, we perform a global sensitivity analysis of the ground-state energies, charge radii, separation energies of selected nuclei for the three LECs in the Hamiltonian, to identify how each LEC contributes to the variances of these observables. It shows that the two-body LEC in the
3S1 channel is the most influential LEC governing these nuclear bulk properties. Finally, the correlations among the ground-state energies of
4He,
12C, and
16O are investigated by varying the LECs in the Hamiltonian. The analysis reveals that the experimental ground-state energies of
12C and
16O cannot be reproduced simultaneously by varying the LECs in the leading-order pionless Hamiltonian. This suggests that additional ingredients in the leading-order Hamiltonian are required to improve its description of light nuclei. The present work establishes an efficient framework for global sensitivity analysis and uncertainty quantification in the quantum Monte Carlo calculations for light and medium-mass nuclei.
To distill the essential elements of nuclear binding, we seek the simplest Hamiltonian capable of modeling atomic nuclei with percent-level accuracy. A critical aspect of this endeavor consists of accurately solving the quantum many-body problem without incurring an exponential computing cost with the number of nucleons. We address this challenge by leveraging a variational Monte Carlo method based on a highly expressive neural-network quantum state ansatz. In addition to computing binding energies and charge radii of nuclei with up to A=20 nucleons, by evaluating their magnetic moments, we demonstrate that neural-network quantum states are able to correctly capture the self-emerging nuclear shell structure. To this end, we introduce a novel computational protocol based on adding an external magnetic field to the nuclear Hamiltonian, which allows the neural network to learn the preferred polarization of the nucleus within the given magnetic field.
We compute ground-state energies and charge radii of light- to medium-mass nuclei with up to
A=58 nucleons, leveraging a variational Monte Carlo method based on Pfaffian-Jastrow neural quantum states. To further understand which elements of the nuclear Hamiltonian are "essential" to predict binding energies and charge radii across the nuclear chart with few-percent errors, we consider different interactions inspired by pionless effective field theory. Specifically, in addition to model "o" of [Phys. Rev. C 103, 054003 (2021)], we study the impact of charge-symmetry-breaking and charge-dependent terms in the nucleon-nucleon force, as well as
p-wave contributions, which have been found to be critical for the stability of
p-shell nuclei. In addition to its intrinsic interest, our work assesses the performance of neural quantum states in the medium-mass regime and examines the impact of these interaction modifications. Using the resulting ground-state simulations, we analyze the computational scaling of variational Monte Carlo with neural quantum states as a function of system size and computational resources, enabling projections for future large-scale calculations.
Nuclear quantum many-body methods rely on integral transform techniques to infer properties of electroweak response functions from ground-state expectation values. Retrieving the energy dependence of these responses is highly non-trivial, especially for quantum Monte Carlo methods, as it requires inverting the Laplace transform -- a notoriously ill-posed problem. In this work, we propose an artificial neural network architecture suitable for accurate response function reconstruction with precise estimation of the uncertainty of the inversion. We demonstrate the capabilities of this new architecture benchmarking it against Maximum Entropy and previously developed neural network methods designed for a similar task, paying particular attention to its robustness against increasing noise in the input Euclidean responses.